1. Classifying Triangles
LESSON 4–1
Classifying Triangles

2. Concept

3. A. Classify the triangle as acute, equiangular, obtuse, or right.
Classify Triangles by Angles
A. Classify the triangle as acute, equiangular, obtuse, or right.
Answer: The triangle has three congruent angles. It is an equiangular triangle.
Example 1A

4. B. Classify the triangle as acute, equiangular, obtuse, or right.
Classify Triangles by Angles
B. Classify the triangle as acute, equiangular, obtuse, or right.
Answer: One angle of the triangle measures 130°, so it is an obtuse angle. The triangle has an obtuse angle, so it is an obtuse triangle.
Example 1B

5. A. ARCHITECTURE The frame of this window design is made up of many triangles. Classify ΔACD.
A. acute
B. equiangular
C. obtuse
D. right
Example 1A

6. B. ARCHITECTURE The frame of this window design is made up of many triangles. Classify ΔADE.
A. acute
B. equiangular
C. obtuse
D. right
Example 1B

7. Answer: Since ΔXYZ has a right angle, it is a right triangle.
Classify Triangles by Angles Within Figures
Classify ΔXYZ as acute, equiangular, obtuse, or right. Explain your reasoning.
Point W is in the interior of XYZ, so by the Angle Addition Postulate, mXYW + mWYZ = mXYZ. By substitution, mXYZ = = 90.
Answer: Since ΔXYZ has a right angle, it is a right triangle.
Example 2

8. Classify ΔACD as acute, equiangular, obtuse, or right.
A. acute
B. equiangular
C. obtuse
D. right
Example 2

9. Concept

10. ARCHITECTURE The frame of this window design is made up of many triangles. Classify ΔABC.
A. isosceles
B. equilateral
C. scalene
D. right
Example 3

11. By the definition of midpoint, VY = YX.
Classify Triangles by Sides Within Figures
If point Y is the midpoint of VX, and WY = 3.0 units, classify ΔVWY as equilateral, isosceles, or scalene. Explain your reasoning.
By the definition of midpoint, VY = YX.
VY + YX = VX Segment Addition Postulate
VY + VY = 8.4 Substitution
2VY = 8.4 Simplify.
VY = 4.2 Divide each side by 2.
Example 4

12. If point C is the midpoint of BD, classify ΔABC as equilateral, isosceles, or scalene.
A. equilateral
B. isosceles
C. scalene
Example 4

13. Finding Missing Values
ALGEBRA Find the measures of the sides of isosceles triangle KLM with base KL. __
Step 1 Find d.
KM = ML Given
4d – 13 = 12 – d Substitution
5d – 13 = 12 Add d to each side.
5d = 25 Add 13 to each side.
d = 5 Divide each side by 5.
Example 5

14. ALGEBRA Find x and the measure of each side of equilateral triangle ABC if AB = 6x – 8, BC = 7 + x, and AC = 13 – x.
A. x = 10; all sides are 3.
B. x = 6; all sides are 13.
C. x = 3; all sides are 10.
D. x = 3; all sides are 16.
Example 5